00:01
Solution to question a, let xi be the random variable which is defined as the amount spent by ith customer in a shop where i is 1, 2, 3 and so on up to 400.
00:17
We are given that e of xi is 650 and also by the definition of s, we know that s is equal to sigma 400, i is equal to 1, xi.
00:35
We need to find the mean mu which is equal to e of s, s is equal to this sigma 400, i is equal to 1, xi which is by some law of expectation e of x, y is equal to e of x plus e of y.
01:06
So, this can be written as sigma 400, i is equal to 1, e of xi which is sigma 650, 400, i is equal to 1.
01:26
This would give us a value 260000.
01:31
So, this is our mean value.
01:35
Next we have to find the standard deviation.
01:37
To do that, we need to find the variance of s.
01:40
Variance of s is variance of s value is this.
01:48
So, sigma 400, i is equal to 1, xi.
01:53
This can be written as sigma 400, i is equal to 1, variance of xi plus 2 sigma 400, i is equal to 1, sigma 400, j is equal to 1, covariance of xi, xi.
02:23
As the amount spent by each customer is independent of others, the covariance of xi, xi for any value is 0.
02:34
So, this will be 0.
02:36
We just have to calculate the variance of sigma xi.
02:40
That will be sigma 400, i is equal to 1.
02:49
Standard deviation is 120, variance is square of standard deviation.
02:53
So, 120 square.
02:55
This will give us the value 5760000.
03:00
Actually, we have to find standard deviation...